Two identical rectangular prisms each have a height of 90 centimeters (cm). The base of each prism is a square, and the surface area of each prism is $\bm{K}$ $cm$${}^{2}$. If the prisms are glued together along a square base, the resulting prism has a surface area of $\frac{92}{47}\bm{K}$ $cm$${}^{2}$. What is the side length, in cm, of each square base?